Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#123×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2705 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×#123×C59 | C2 |
| hypercenter | C2×#123 | D59 |
| hypocenter | C59 | #2705 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=ef,b^2=f,c^2=e,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28795707, #28795718, #28795768, … |
| maximal normal subgroup of | #28795707, #28795718, #28795768, … |
| maximal quotient of | #28516010, #28516159, #28516212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 11179);